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Full text of "Rapid Population Growth Consequences And Policy Implications"

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Effect of Change in Age-Specific Birth Rates on Stable Population Parameters
Ar =
e rxpx AZ> = bAAr = bA - Am.
K.                     *
Ad = (bA - 1) Ar
e'rxpx =  (bA  -  1)--------  Am
----- = (A - a)--------Am,
K                x
mx = age-specific birth rate at age x
r = intrinsic rate of natural increase
b = intrinsic birth rate
d - intrinsic death rate
PX =  ^jc/'o   = Probability of living from birth to age ^
c^da = be~rap^da = proportion of population between ages a and a + da
K = aj ae~rapamada = mean age of childbearing in the stable population
w                     w
A =    J    ae~rapada/ j    e~mpada = mean age in stable population
or2 = b /    (t - A^e'rtpjdt = variance of age distribution in stable population
a = youngest age of childbearing
j3 = oldest age of childbearing
GJ = oldest age to which anyone lives
is based on national publications, correspondence with the statistical agencies of about forty countries, and the very helpful United Nations Demographic Yearbook, especially the 1967 edition (1). An extended discussion of these data, and footnotes to their sources, appears in Population, which also contains a full description of the methods by which the uniform life tables, intrinsic and standardized rates, and other derived information, were calculated. I am grateful to W. H. Freeman for permission to use this material anH the tp.vt that discusses it. of how the table is to be read, if the birth rate mx increases by the quantity Arax, the effect of this on r, the intrinsic rate of natural increase, is an increase of Ar = e~rxpxAmx/K., where px is the probability of living to age x for a child just born, and K. is the mean age of childbearing in the stable population. Further down, the fractional effect of the change in the birth rate at age x on the proportion ca of the population at age a is given as this same value of Ar multiplied by A -a, where A is the mean age in the stable population.